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Prime Minister John Key and Foreign Minister Murray McCully will start campaigning in force for former rival Helen Clark this week, travelling overseas to push her case for the United Nations Secretary-General role.

Mr Key will travel to China with a trade delegation tomorrow and says he will raise Helen Clark's candidacy in his formal meeting with President Xi Jinping and Premier Li Keqiang.

"I will be reaffirming not only her credentials but her strong commitment to China and the role that she played in the signing of the China FTA [free-trade agreement]."

As one of the five permanent members of the Security Council, China has a critical role in the process of appointing the Secretary-General.

Mr McCully leaves this weekend for the UN in New York and will then visit Britain, Germany and France. He said he would use the opportunity to support Helen Clark's candidacy in his meetings with foreign ministers.

Yesterday, Helen Clark made her first appearance before the UN General Assembly as a candidate. Her session went beyond the two-hour limit and, possibly because of her high-profile role as head of the United Nations Development Programme, she attracted more questions than any of the other eight candidates.

Some commentators have suggested the big powers will want a more compliant Secretary-General than a former Prime Minister, and Helen Clark deployed some subtle flattery of the countries' leaders in a bid to quell that, saying she had met many of those leaders "and I have listened to and learned from them".

She rejected a suggestion she was an "establishment candidate" because of her role at the UNDP, saying she had "come from the outside of everything I have done". She cited her success as a woman politician "breaking into a man's world" to become the first woman appointed Administrator of the UNDP.

Asked afterwards about a British betting agency rating her as the favourite, Helen Clark said she was not a betting woman. She also sought to blunt the question of whether an Eastern European candidate should get the job, saying the more-open process allowed member states a greater say. "This is part of ensuring the best person for the job is selected."

Margaret Besheer, UN correspondent for the Voice of America, said the day had left Helen Clark well placed. "She certainly is a front runner and she's in a very good position after today, I would say."

The Security Council will meet in July for an initial straw poll on each candidate. Further candidates may put their names forward before then, possibly including former Australian Prime Minister Kevin Rudd.